# Conformal Prediction for Dyadic Regression Under Complex Missingness

arXiv: https://arxiv.org/abs/2606.11136 · HTML: https://mlsanity.com/paper/2606.11136/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 61 references that are in the map.
- First posted on arXiv 9 Jun 2026.

## Builds on (most cited first, 11 of 11)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Exchangeability, Conformal Prediction, and Rank Tests](https://mlsanity.com/paper/2005.06095/) (2020)
- [Multivariate Conformal Prediction using Optimal Transport](https://mlsanity.com/paper/2502.03609/) (2025)
- [Measuring Evidence against Exchangeability and Group Invariance with E-values](https://mlsanity.com/paper/2310.01153/) (2023)
- [Distribution-Free Matrix Prediction Under Arbitrary Missing Pattern](https://mlsanity.com/paper/2305.11640/) (2023)
- [On the Validity of Conformal Prediction for Network Data Under Non-Uniform Sampling](https://mlsanity.com/paper/2306.07252/) (2023)
- [Multivariate quantile-based permutation tests with application to functional data](https://mlsanity.com/paper/2311.04017/) (2023)
- [Randomization Inference: Theory and Applications](https://mlsanity.com/paper/2406.09521/) (2024)
- [Conformal Network Link Prediction with False Discovery Rate Control under Unstructured Missingness](https://mlsanity.com/paper/2507.07025/) (2025)
- [Conditional Predictive Inference for General Structured Data with Group Symmetries](https://mlsanity.com/paper/2605.17934/) (2026)
- [Data augmented bootstrap: Unifying confidence interval construction by approximate invariance](https://mlsanity.com/paper/2606.09049/) (2026)

## Built on by (most cited first, 1 of 1)

- [The Exceedance Design Effect: Effective Sample Size for Thresholds under Clustering](https://mlsanity.com/paper/2608.21262/) (2026)

## Abstract (arXiv)

We develop a framework for conformal prediction in dyadic regression problems under complex missingness mechanisms. At the theoretical level, we develop general technical tools for establishing finite-sample validity of conformal prediction under distributional invariance conditions weaker than exchangeability. A key result handles the case where the sample itself is a random subset of the index set, a setting not covered by existing theory. In addition, we propose conformal prediction procedures for jointly exchangeable arrays, including full conformal, split conformal, a row-column approach exploiting similarities within rows and columns, and a selective conformal procedure achieving mask-conditional validity. For missing elements, we establish asymptotic validity of a weighted conformal procedure under a nonparametric graphon model for the missingness mechanism. We further establish conditional validity results for both continuous and discrete responses; to the best of our knowledge, this is the first formal proof of asymptotic conditional validity for weighted conformal prediction under a missing-not-at-random assumption. The proposed methods are illustrated on synthetic and real network data.